Sub-nanometer length metrology for ultra-stable ring laser gyroscopes

Large-frame ring laser gyroscopes are extremely sensitive inertial detectors of rotational motion. When properly coupled to the ground, they provide precise measurements of the Earth rotation rate and give important informations to geodesy and geophysics. Recent advances in this technology led to consider the application of ring laser gyroscopes to fundamental physics. In this context is GINGER (Gyroscopes IN GEneral Relativity), a scientic proposal for testing General Relativity (local observation of the Lense-Thirring eect) with a ground-based array of ring laser gyroscopes. The experimental target is to locally measure the Earth rotation rate with a relative precision better than one part in 109, corresponding to an absolute rotational resolution of 10−14 rad/s. The main factor limiting the performances of the presently most stable ring laser gyroscopes is the uncontrolled deformation of their optical cavity, since instabilities in the cavity geometry introduce systematic errors in the rotational signal. Cavity geometry is typically kept stable by using monolithic frames made of ultra-low thermal expansion materials, and operating in very well isolated environments. An alternative approach is based on the active control of the shape in heterolithic cavities, by measuring and stabilizing the mirrors positions by means of laser-based length metrology. The goal of this thesis is the development of a stabilization system based on interferometric length metrology, with a view to improve the sensitivity of the new generation square ring laser gyroscopes, going beyond the level achievable with passive methods. The main idea proposed in this work is to exploit the diagonal resonators formed by opposite cavity mirrors, and to use their lengths as observables to constraint, against an optical reference standard, residual deformation degrees of freedom of the square cavity. As a rst step, a detailed model of the light propagation along the square cavity has been developed. This allowed us to quantify the eectiveness of the v xed length constraint of the diagonal resonators, and gave precise indications for the optimization strategy of the residual degrees of freedom. The optical frequency reference is a helium neon laser stabilized to the iodine molecular absorption. Since the power emitted by this laser is of only 300 µW, an optical amplier, based on the injection locking of a 15 mW diode laser, has been developed to guarantee a proper signal to noise ratio in the interferometric absolute length measurements. To stabilize the absolute lengths of the two diagonals, we proposed an original experimental method for the determination of both the optical resonance frequency and the free spectral range of each cavity. It is based on a triple-frequency modulation of the interrogating laser beam by electro-optic modulators. In a rst tabletop experiment, the method has been veried on two Fabry-Perot resonators that, composed by couples of spherical mirrors typically used in the He-Ne ring cavities, simulate the diagonals of a ring laser gyroscope on an optical bench. Here, the capability of setting equal the two lengths at the level of 500 nm, with residual uctuations only limited by the laser frequency noise, has been experimentally proved. As a nal result, we have applied the developed method to lock the diagonal cavities lengths of GP2 ring laser gyroscope, a square cavity 1.6 m in side length dedicated to the interferometric control of the cavity geometry deformations, and fully set up at the INFN laboratories in Pisa in June 2015